Internal problem ID [591]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 18
dsolve(2*cos(x)*sin(x)*sin(y(x))+cos(y(x))*sin(x)^2*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\arcsin \left (\frac {2 c_{1}}{-1+\cos \left (2 x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 5.176 (sec). Leaf size: 21
DSolve[2*Cos[x]*Sin[x]*Sin[y[x]]+Cos[y[x]]*Sin[x]^2*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {1}{2} c_1 \csc ^2(x)\right ) y(x)\to 0 \end{align*}